Example Run
| Image | U | possible edges | V \ U | Description |
|---|---|---|---|---|
| {} | {A,B,C,D,E,F,G} | This is our original weighted graph. The numbers near the edges indicate their weight. | ||
| {D} | {D,A} = 5 V {D,B} = 9 {D,E} = 15 {D,F} = 6 |
{A,B,C,E,F,G} | Vertex D has been arbitrarily chosen as a starting point. Vertices A, B, E and F are connected to D through a single edge. A is the vertex nearest to D and will be chosen as the second vertex along with the edge AD. | |
| {A,D} | {D,B} = 9 {D,E} = 15 {D,F} = 6 V {A,B} = 7 |
{B,C,E,F,G} | The next vertex chosen is the vertex nearest to either D or A. B is 9 away from D and 7 away from A, E is 15, and F is 6. F is the smallest distance away, so we highlight the vertex F and the edge DF. | |
| {A,D,F} | {D,B} = 9 {D,E} = 15 {A,B} = 7 V {F,E} = 8 {F,G} = 11 |
{B,C,E,G} | The algorithm carries on as above. Vertex B, which is 7 away from A, is highlighted. | |
| {A,B,D,F} | {B,C} = 8 {B,E} = 7 V {D,B} = 9 cycle {D,E} = 15 {F,E} = 8 {F,G} = 11 |
{C,E,G} | In this case, we can choose between C, E, and G. C is 8 away from B, E is 7 away from B, and G is 11 away from F. E is nearest, so we highlight the vertex E and the edge BE. | |
| {A,B,D,E,F} | {B,C} = 8 {D,B} = 9 cycle {D,E} = 15 cycle {E,C} = 5 V {E,G} = 9 {F,E} = 8 cycle {F,G} = 11 |
{C,G} | Here, the only vertices available are C and G. C is 5 away from E, and G is 9 away from E. C is chosen, so it is highlighted along with the edge EC. | |
| {A,B,C,D,E,F} | {B,C} = 8 cycle {D,B} = 9 cycle {D,E} = 15 cycle {E,G} = 9 V {F,E} = 8 cycle {F,G} = 11 |
{G} | Vertex G is the only remaining vertex. It is 11 away from F, and 9 away from E. E is nearer, so we highlight G and the edge EG. | |
| {A,B,C,D,E,F,G} | {B,C} = 8 cycle {D,B} = 9 cycle {D,E} = 15 cycle {F,E} = 8 cycle {F,G} = 11 cycle |
{} | Now all the vertices have been selected and the minimum spanning tree is shown in green. In this case, it has weight 39. |
Read more about this topic: Prim's Algorithm
Famous quotes containing the word run:
“She had been getting ready for her great journey to the horizons in search of people; it was important to all the world that she should find them and they find her, but she had been whipped like a cur dog, and run off down a back road after things.”
—Zora Neale Hurston (1891–1960)
“Religious literature has eminent examples, and if we run over our private list of poets, critics, philanthropists and philosophers, we shall find them infected with this dropsy and elephantiasis, which we ought to have tapped.”
—Ralph Waldo Emerson (1803–1882)